>> Here's the table which shows the amount of money spent on books and maps in the United States for the years 1990 to 2000. Let's use the information and generate a scatter plot and decide on an appropriate model for the information and actually generate the model to see how well it fits. Well, let's see, let's first enter the information and to do that we'll press stat and then to edit we'll press enter and notice that the information has already been entered. The important thing here is to realize that in this column where the years would be entered I have only used the last digit for the year so this would be 1990; this is 1991 and so on and so the base's year for our study here is the year 1990. Okay, let's take a look at the scatter plot with the information entered we press second and then Y equals and we want to turn the plot on and I'll do that just by pressing enter here. I'm noticing that all of the other items are on the default and our information for X and Y values are in L1 and L2 and now we're ready to look at the scatter plot. Let's make the calculator set up the window for us I'll cursor down to item 9 here zoom stat and here is our information. Now, notice that this particular scatter plot isn't as obviously quadratic in nature that is the model which will best fit this is not necessarily quadratic it kind of looks like it could be linear, you see, that this could be thought of as linear it's just slightly curvy here so maybe a quadratic model is appropriate as well. Let's take a look at both of them let's go through the process of calculating I'm pressing stat and then the right arrow and I'll go down to the linear regression model first and pressing enter I get the linear regression. Wow, it kind of looks like it's a pretty good fit doesn't it because after all these values are close to 1 for R and R squared so we might think, gee, we have a pretty good fit. Let's take a look at the graph and we'll press Y equals and then make the calculator bring the equation on board. I'm going down here to item 5 and then cursor over 2 and pressing enter and here's the equation and now for the graph. Gee, the linear equation, the graph of the linear equation seems to fit fairly well but let's go through the process for a different kind of model. How about the quadratic model? Well, let's see, we'll press stat and then calculate and now we want the quadratic regression, here it is pressing enter and then enter again. Now, before I press enter again I want us to notice the R and R squared values here, you see, 9 point 8, 6 here 9 point 7, 2. Now, we're gonna compare that with corresponding values for the quadratic regression. Oh, look R squared is point 9, 9, 5 and that's a good deal closer than the value for the linear regression so this line ought to fit better; this graph ought to fit better. Now, to cause the calculator to bring it on board I'll have to cursor down here to Y2 and then make the request for the regression equation and to do that vares [assumed spelling] and then down to statistics and over to the right 2. Now, it's important to realize this is exactly where we went before to grab the linear model we go to the same place for the quadratic model. You see the calculator replaces the previous regression equation each time it makes a new calculation so now the quadratic model is on board and here is its graph and here it comes overlaid with the linear graph. Now if we just want to see one of the graphs and see how well it fits we can do that by going back to Y equals and I'm pressing the left arrow button and with the icon blinking over the equal sign I can press the enter and now I have deselected this particular graph and when I go back to the graph I'll see only the quadratic model and it really seems to fit the information well. Well, at this point we could make any number of calculations the corresponding a year with some amount of money spent on books and maps but the main theme of this problem was to choose a model and see how well it fits and we've done that.